Yes mice do communicate with each other by squeaking.
Mice also sometimes squeak when they are scared which also alerts other mice that danger is around.
The mouses squeaks can be different depending on what they are communicating just like a dogs bark or a cats meow can vary sometimes depending on what they are saying to each other.
Sometimes mice can squeak so low that you may not hear it and other times they squeak loud enough that you can hear it.
Cats have a pretty good sense of hearing and can hear a mouse squeaking quieter than a human can hear.
So if you have a cat or dog they may hear the mouse squeak and look around trying to find it when you may not hear it.